The dynamical RLL conjecture for elliptic L-operators

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Let Uq,p([...??]U_{q,p}([...??] be the elliptic quantum algebra with half currents assembled into the LL-operator [...??][...??]. For two auxiliary tensor components, write [...??][...??] and let R+(z1/z2,[...??])R^+(z_1/z_2,[...??]) and R+∗(z1/z2,[...??])R^{+*}(z_1/z_2,[...??]) denote the corresponding dynamical RR-matrices. Dynamical RLL conjecture. The LL-operator satisfies

R+(12)(z1/z2,[...??])[...??][...??]=[...??][...??]R+∗(12)(z1/z2,[...??]).R^{+(12)}(z_1/z_2,[...??])[...??][...??]=[...??][...??]R^{+*(12)}(z_1/z_2,[...??]).

This conjecture proposes the exchange relation governing the elliptic LL-operator and is intended to provide its dynamical RLLRLL presentation. The supplied text does not state whether the relation has been proved or remains open.

References

Primary source

Hitoshi Konno, “Elliptic Weight Functions and Elliptic q-KZ Equation”, arXiv:1706.07630 (2017).

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